Pairwise Markov chains and Bayesian unsupervised fusion

Abstract

We propose a new model called a Pairwise Markov Chain (PMC), which generalises the classical Hidden Markov Chain (HMC) model. The PMC model is more general than HMC in that the process one wants to estimate is not necessarily a Markov process. However, PMC allows one to use the classical Bayesian restoration methods like Maximum A Posteriori (MAP), or Maximal Posterior Mode (MPM). So, akin to HMC, PMC allows one to restore hidden stochastic processes, with numerous applications to speech recognition, multisensor image segmentation, among others. Furthermore, we propose a new method of parameter estimation, which allows one to perform unsupervised restoration with PMC. The method proposed is valid even with non Gaussian and possibly correlated noise. Furthermore, the very form of the statistical distribution of the noise need not be known exactly. All that is required is that for each class the form of the noise distribution belongs to a given set of forms.